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arXiv · 2506.09017

Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings

Daniel P. Bossaller·Hiram H. López
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Abstract

Codes over rings, especially over Galois rings, have been extensively studied for nearly three decades due to their similarity to linear codes over finite fields. A distributed storage system uses a linear code to encode a large file across several nodes. If one of the nodes fails, a linear exact repair scheme efficiently recovers the failed node by accessing and downloading data from the rest of the servers of the storage system. In this article, we develop a linear repair scheme for free maximum distance separable codes, which coincide with free maximum distance with respect to the rank codes over Galois rings. In particular, we give a linear repair scheme for full-length Reed-Solomon codes over a Galois ring.

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Daniel P. Bossaller, Hiram H. López. 2025-06-10. Linear exact repair schemes for free MDS and Reed-Solomon codes over Galois rings. https://arxiv.org/abs/2506.09017

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